Question

Which of the following is the correct graph of the compound inequality 4p + 1 > −11 or 6p + 3 < 39?

A. a number line with closed circles at negative 3 and 6 and shading in between.
B. number line with open dot at negative 3 with shading to the left and an open dot at 6 with shading to the right.
C. number line with open dots at negative 2 and 5 with shading in between.
D. number line with shading everywhere.

Answer 1

D. Number line with shading everywhere

1. p>-3

2. p<6

Explanation:

1. 4p+1>-11

Subtract by 1 both sides of equation.

4p+1-1>-11+1

Simplify.

4p>-12

Divide by 4 from both sides of equation.

4p/4>-12/4

Simplify, to find the answer.

-12/4=-3

p>-3 is the correct answer.

____________________________

2. 6p+3<39

Subtract by 3 from both sides of equatoin.

6p+3-3<39-3

Simplify.

39-3=36

6p<36

Divide by 6 from both sides of equation.

6p/6<36/6

Simplify, to find the answer.

36/6=6

p<6 is the correct answer.

D is the correct answer.

Answer 2

B. Number line with open dot at negative 3 with shading to the left and an open dot at 6 with shading to the right.

Explanation:

Given compound inequality,

4p + 1 > −11 or 6p + 3 < 39,

4p > - 11 - 1 or 6p < 39 - 3

4p > -12 or 6p < 36

p > -3 or p < 6

⇒ -3 < p < 6

⇒ (-3 6)

That is, number line with open dot at negative 3 with shading to the left and an open dot at 6 with shading to the right.

Option 'B' is correct.